ATMW Topology (2013)

Schedule of Lectures: (04^th to 09^th Feb 2013)

List of resource persons:

1. Samik Basu, Vivekananda University, Belur
2. Goutam Mukherjee, ISI, Kolkata
3. A. R. Shastri, IIT Bombay, Mumbai

List of courses:

The following three courses are being planned:

• On homotopy groups of spheres.
• On Steenrod algebra and its dual (and applications, if there is time).
• On the complex cobordism ring and the formal group law (with applications, if there is time).

Details of courses:

Homotopy groups of spheres:
Leray-Serre spectral sequence, Serre class of abelian groups, finiteness of homotopy groups π_m (Sⁿ ) when m <> n if n is odd (m <> n, 2n − 1 if n is even), Freudenthal suspension theorem, stable homotopy groups of spheres. Postnikov factorization (if time permits).

Steenrod algebra and its dual:
Axioms for the Steenrod operation, The Eilenberg-MacLane spaces, mod-2 cohomology algebra of K(Z/2Z, n). The Steenrod algebra, the dual of the Steenrod algebra, the Hopf algebra structure.

Complex cobordism and formal group law:
Unoriented and oriented cobordism, Complex cobordism, Characteristic numbers, Chern numbers. Bordism theory as via spectra. The structure of the complex cobordism ring. Formal group law–examples. The Lazard ring. Quillen’s theorem. (If there is time, BP cohomology will be discussed.)